Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
Ocean currents, prevailing winds, and the hierarchical structures of river networks are known to create asymmetries in re-colonization between habitat patches. The impacts of such asymmetries on metapopulation persistence are seldom considered, especially ...
The spectrum of exponentially weighted covariance matrices is studied here. We first give a formal way of obtaining the spectrum using annealed approximation frequently used in Statistical Mechanics. Using the method developed by Bai and Silverstein we obt ...
n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r^{-alpha} and random phase cha ...
We derive an information-theoretic upper bound on the rate per communication pair in a large ad hoc wireless network. We show that under minimal conditions on the attenuation due to the environment and for networks with a constant density of users, this ra ...
We provide a tight approximate characterization of the n-dimensional product multicommodity flow (PMF) region for a wireless network of n nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in bo ...
We study a class of hyperbolic stochastic partial di®erential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spat ...
We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, that includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficien ...
The capacity scaling of extended two-dimensional wireless networks is known in the high attenuation regime, i.e. when the power path loss exponent alpha is greater than 4. This has been accomplished by deriving information theoretic upper bounds for this r ...
n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of 1/r^alpha as well as a random phase. We identify exactly ...
Ce cours est un cours de niveau master donnant une introduction au calcul stochastique, avec rappel de probabilités et applications aux mathématiques financières. ...